LMFDB - Group of Dirichlet characters of modulus 16184

Show commands: PariGP / SageMath

sage: H = DirichletGroup(16184)

pari: g = idealstar(,16184,2)

Character group

sage: G.order() pari: g.no
Order	=	6528
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{816}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{16184}(4047,\cdot)$, $\chi_{16184}(8093,\cdot)$, $\chi_{16184}(2313,\cdot)$, $\chi_{16184}(1737,\cdot)$

First 32 of 6528 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{16184}(1,\cdot)$	16184.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{16184}(3,\cdot)$	16184.ga	816	yes	$-1$	$1$	$e\left(\frac{139}{816}\right)$	$e\left(\frac{143}{816}\right)$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{613}{816}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{361}{408}\right)$	$e\left(\frac{533}{816}\right)$	$e\left(\frac{143}{408}\right)$	$e\left(\frac{139}{272}\right)$
$\chi_{16184}(5,\cdot)$	16184.gc	816	yes	$1$	$1$	$e\left(\frac{143}{816}\right)$	$e\left(\frac{379}{816}\right)$	$e\left(\frac{143}{408}\right)$	$e\left(\frac{161}{816}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{185}{408}\right)$	$e\left(\frac{337}{816}\right)$	$e\left(\frac{379}{408}\right)$	$e\left(\frac{143}{272}\right)$
$\chi_{16184}(9,\cdot)$	16184.fu	408	no	$1$	$1$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{143}{408}\right)$	$e\left(\frac{139}{204}\right)$	$e\left(\frac{205}{408}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{3}{136}\right)$
$\chi_{16184}(11,\cdot)$	16184.fx	816	yes	$1$	$1$	$e\left(\frac{613}{816}\right)$	$e\left(\frac{161}{816}\right)$	$e\left(\frac{205}{408}\right)$	$e\left(\frac{499}{816}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{211}{408}\right)$	$e\left(\frac{563}{816}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{69}{272}\right)$
$\chi_{16184}(13,\cdot)$	16184.dw	68	yes	$-1$	$1$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{11}{68}\right)$
$\chi_{16184}(15,\cdot)$	16184.eu	136	no	$-1$	$1$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{5}{136}\right)$
$\chi_{16184}(19,\cdot)$	16184.fs	408	yes	$1$	$1$	$e\left(\frac{361}{408}\right)$	$e\left(\frac{185}{408}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{211}{408}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{89}{136}\right)$
$\chi_{16184}(23,\cdot)$	16184.fy	816	no	$1$	$1$	$e\left(\frac{533}{816}\right)$	$e\left(\frac{337}{816}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{563}{816}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{811}{816}\right)$	$e\left(\frac{337}{408}\right)$	$e\left(\frac{261}{272}\right)$
$\chi_{16184}(25,\cdot)$	16184.fu	408	no	$1$	$1$	$e\left(\frac{143}{408}\right)$	$e\left(\frac{379}{408}\right)$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{337}{408}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{7}{136}\right)$
$\chi_{16184}(27,\cdot)$	16184.fi	272	yes	$-1$	$1$	$e\left(\frac{139}{272}\right)$	$e\left(\frac{143}{272}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{69}{272}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{145}{272}\right)$
$\chi_{16184}(29,\cdot)$	16184.fl	272	no	$-1$	$1$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{19}{272}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{131}{272}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{239}{272}\right)$
$\chi_{16184}(31,\cdot)$	16184.gd	816	no	$-1$	$1$	$e\left(\frac{571}{816}\right)$	$e\left(\frac{335}{816}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{757}{816}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{325}{408}\right)$	$e\left(\frac{173}{816}\right)$	$e\left(\frac{335}{408}\right)$	$e\left(\frac{27}{272}\right)$
$\chi_{16184}(33,\cdot)$	16184.eo	102	no	$-1$	$1$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{13}{17}\right)$
$\chi_{16184}(37,\cdot)$	16184.fz	816	yes	$-1$	$1$	$e\left(\frac{251}{816}\right)$	$e\left(\frac{631}{816}\right)$	$e\left(\frac{251}{408}\right)$	$e\left(\frac{605}{816}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{329}{408}\right)$	$e\left(\frac{349}{816}\right)$	$e\left(\frac{223}{408}\right)$	$e\left(\frac{251}{272}\right)$
$\chi_{16184}(39,\cdot)$	16184.fy	816	no	$1$	$1$	$e\left(\frac{727}{816}\right)$	$e\left(\frac{155}{816}\right)$	$e\left(\frac{319}{408}\right)$	$e\left(\frac{673}{816}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{397}{408}\right)$	$e\left(\frac{281}{816}\right)$	$e\left(\frac{155}{408}\right)$	$e\left(\frac{183}{272}\right)$
$\chi_{16184}(41,\cdot)$	16184.fj	272	no	$1$	$1$	$e\left(\frac{35}{272}\right)$	$e\left(\frac{127}{272}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{53}{272}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{105}{272}\right)$
$\chi_{16184}(43,\cdot)$	16184.eq	136	no	$-1$	$1$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{67}{136}\right)$
$\chi_{16184}(45,\cdot)$	16184.gc	816	yes	$1$	$1$	$e\left(\frac{421}{816}\right)$	$e\left(\frac{665}{816}\right)$	$e\left(\frac{13}{408}\right)$	$e\left(\frac{571}{816}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{91}{408}\right)$	$e\left(\frac{587}{816}\right)$	$e\left(\frac{257}{408}\right)$	$e\left(\frac{149}{272}\right)$
$\chi_{16184}(47,\cdot)$	16184.fc	204	no	$1$	$1$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{31}{204}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{7}{68}\right)$
$\chi_{16184}(53,\cdot)$	16184.fq	408	yes	$1$	$1$	$e\left(\frac{377}{408}\right)$	$e\left(\frac{109}{408}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{239}{408}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{91}{408}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{105}{136}\right)$
$\chi_{16184}(55,\cdot)$	16184.dy	68	no	$1$	$1$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{53}{68}\right)$
$\chi_{16184}(57,\cdot)$	16184.fm	272	no	$-1$	$1$	$e\left(\frac{15}{272}\right)$	$e\left(\frac{171}{272}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{73}{272}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{45}{272}\right)$
$\chi_{16184}(59,\cdot)$	16184.fs	408	yes	$1$	$1$	$e\left(\frac{11}{408}\right)$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{185}{408}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{277}{408}\right)$	$e\left(\frac{139}{204}\right)$	$e\left(\frac{11}{136}\right)$
$\chi_{16184}(61,\cdot)$	16184.gc	816	yes	$1$	$1$	$e\left(\frac{233}{816}\right)$	$e\left(\frac{589}{816}\right)$	$e\left(\frac{233}{408}\right)$	$e\left(\frac{599}{816}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{407}{408}\right)$	$e\left(\frac{7}{816}\right)$	$e\left(\frac{181}{408}\right)$	$e\left(\frac{233}{272}\right)$
$\chi_{16184}(65,\cdot)$	16184.dr	48	no	$-1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{48}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{16184}(67,\cdot)$	16184.eg	102	yes	$-1$	$1$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{16184}(69,\cdot)$	16184.cw	34	yes	$-1$	$1$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{8}{17}\right)$
$\chi_{16184}(71,\cdot)$	16184.fk	272	no	$1$	$1$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{101}{272}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{63}{272}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{55}{272}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{91}{272}\right)$
$\chi_{16184}(73,\cdot)$	16184.gb	816	no	$1$	$1$	$e\left(\frac{631}{816}\right)$	$e\left(\frac{611}{816}\right)$	$e\left(\frac{223}{408}\right)$	$e\left(\frac{505}{816}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{133}{408}\right)$	$e\left(\frac{497}{816}\right)$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{87}{272}\right)$
$\chi_{16184}(75,\cdot)$	16184.dn	48	no	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{48}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{16184}(79,\cdot)$	16184.fy	816	no	$1$	$1$	$e\left(\frac{365}{816}\right)$	$e\left(\frac{217}{816}\right)$	$e\left(\frac{365}{408}\right)$	$e\left(\frac{779}{816}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{311}{408}\right)$	$e\left(\frac{67}{816}\right)$	$e\left(\frac{217}{408}\right)$	$e\left(\frac{93}{272}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$16184$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{816}\)
Order	$6528$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{16184}(1,\cdot)\)	16184.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{16184}(3,\cdot)\)	16184.ga	816	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{816}\right)\)	\(e\left(\frac{143}{816}\right)\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{613}{816}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{361}{408}\right)\)	\(e\left(\frac{533}{816}\right)\)	\(e\left(\frac{143}{408}\right)\)	\(e\left(\frac{139}{272}\right)\)
\(\chi_{16184}(5,\cdot)\)	16184.gc	816	yes	\(1\)	\(1\)	\(e\left(\frac{143}{816}\right)\)	\(e\left(\frac{379}{816}\right)\)	\(e\left(\frac{143}{408}\right)\)	\(e\left(\frac{161}{816}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{185}{408}\right)\)	\(e\left(\frac{337}{816}\right)\)	\(e\left(\frac{379}{408}\right)\)	\(e\left(\frac{143}{272}\right)\)
\(\chi_{16184}(9,\cdot)\)	16184.fu	408	no	\(1\)	\(1\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{143}{408}\right)\)	\(e\left(\frac{139}{204}\right)\)	\(e\left(\frac{205}{408}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{3}{136}\right)\)
\(\chi_{16184}(11,\cdot)\)	16184.fx	816	yes	\(1\)	\(1\)	\(e\left(\frac{613}{816}\right)\)	\(e\left(\frac{161}{816}\right)\)	\(e\left(\frac{205}{408}\right)\)	\(e\left(\frac{499}{816}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{211}{408}\right)\)	\(e\left(\frac{563}{816}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{69}{272}\right)\)
\(\chi_{16184}(13,\cdot)\)	16184.dw	68	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{11}{68}\right)\)
\(\chi_{16184}(15,\cdot)\)	16184.eu	136	no	\(-1\)	\(1\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{5}{136}\right)\)
\(\chi_{16184}(19,\cdot)\)	16184.fs	408	yes	\(1\)	\(1\)	\(e\left(\frac{361}{408}\right)\)	\(e\left(\frac{185}{408}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{211}{408}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{89}{136}\right)\)
\(\chi_{16184}(23,\cdot)\)	16184.fy	816	no	\(1\)	\(1\)	\(e\left(\frac{533}{816}\right)\)	\(e\left(\frac{337}{816}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{563}{816}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{811}{816}\right)\)	\(e\left(\frac{337}{408}\right)\)	\(e\left(\frac{261}{272}\right)\)
\(\chi_{16184}(25,\cdot)\)	16184.fu	408	no	\(1\)	\(1\)	\(e\left(\frac{143}{408}\right)\)	\(e\left(\frac{379}{408}\right)\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{337}{408}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{7}{136}\right)\)
\(\chi_{16184}(27,\cdot)\)	16184.fi	272	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{272}\right)\)	\(e\left(\frac{143}{272}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{69}{272}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{145}{272}\right)\)
\(\chi_{16184}(29,\cdot)\)	16184.fl	272	no	\(-1\)	\(1\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{19}{272}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{131}{272}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{239}{272}\right)\)
\(\chi_{16184}(31,\cdot)\)	16184.gd	816	no	\(-1\)	\(1\)	\(e\left(\frac{571}{816}\right)\)	\(e\left(\frac{335}{816}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{757}{816}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{325}{408}\right)\)	\(e\left(\frac{173}{816}\right)\)	\(e\left(\frac{335}{408}\right)\)	\(e\left(\frac{27}{272}\right)\)
\(\chi_{16184}(33,\cdot)\)	16184.eo	102	no	\(-1\)	\(1\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{13}{17}\right)\)
\(\chi_{16184}(37,\cdot)\)	16184.fz	816	yes	\(-1\)	\(1\)	\(e\left(\frac{251}{816}\right)\)	\(e\left(\frac{631}{816}\right)\)	\(e\left(\frac{251}{408}\right)\)	\(e\left(\frac{605}{816}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{329}{408}\right)\)	\(e\left(\frac{349}{816}\right)\)	\(e\left(\frac{223}{408}\right)\)	\(e\left(\frac{251}{272}\right)\)
\(\chi_{16184}(39,\cdot)\)	16184.fy	816	no	\(1\)	\(1\)	\(e\left(\frac{727}{816}\right)\)	\(e\left(\frac{155}{816}\right)\)	\(e\left(\frac{319}{408}\right)\)	\(e\left(\frac{673}{816}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{397}{408}\right)\)	\(e\left(\frac{281}{816}\right)\)	\(e\left(\frac{155}{408}\right)\)	\(e\left(\frac{183}{272}\right)\)
\(\chi_{16184}(41,\cdot)\)	16184.fj	272	no	\(1\)	\(1\)	\(e\left(\frac{35}{272}\right)\)	\(e\left(\frac{127}{272}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{53}{272}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{105}{272}\right)\)
\(\chi_{16184}(43,\cdot)\)	16184.eq	136	no	\(-1\)	\(1\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{67}{136}\right)\)
\(\chi_{16184}(45,\cdot)\)	16184.gc	816	yes	\(1\)	\(1\)	\(e\left(\frac{421}{816}\right)\)	\(e\left(\frac{665}{816}\right)\)	\(e\left(\frac{13}{408}\right)\)	\(e\left(\frac{571}{816}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{91}{408}\right)\)	\(e\left(\frac{587}{816}\right)\)	\(e\left(\frac{257}{408}\right)\)	\(e\left(\frac{149}{272}\right)\)
\(\chi_{16184}(47,\cdot)\)	16184.fc	204	no	\(1\)	\(1\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{31}{204}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{7}{68}\right)\)
\(\chi_{16184}(53,\cdot)\)	16184.fq	408	yes	\(1\)	\(1\)	\(e\left(\frac{377}{408}\right)\)	\(e\left(\frac{109}{408}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{239}{408}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{91}{408}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{105}{136}\right)\)
\(\chi_{16184}(55,\cdot)\)	16184.dy	68	no	\(1\)	\(1\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{53}{68}\right)\)
\(\chi_{16184}(57,\cdot)\)	16184.fm	272	no	\(-1\)	\(1\)	\(e\left(\frac{15}{272}\right)\)	\(e\left(\frac{171}{272}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{73}{272}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{45}{272}\right)\)
\(\chi_{16184}(59,\cdot)\)	16184.fs	408	yes	\(1\)	\(1\)	\(e\left(\frac{11}{408}\right)\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{185}{408}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{277}{408}\right)\)	\(e\left(\frac{139}{204}\right)\)	\(e\left(\frac{11}{136}\right)\)
\(\chi_{16184}(61,\cdot)\)	16184.gc	816	yes	\(1\)	\(1\)	\(e\left(\frac{233}{816}\right)\)	\(e\left(\frac{589}{816}\right)\)	\(e\left(\frac{233}{408}\right)\)	\(e\left(\frac{599}{816}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{407}{408}\right)\)	\(e\left(\frac{7}{816}\right)\)	\(e\left(\frac{181}{408}\right)\)	\(e\left(\frac{233}{272}\right)\)
\(\chi_{16184}(65,\cdot)\)	16184.dr	48	no	\(-1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{16184}(67,\cdot)\)	16184.eg	102	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{16184}(69,\cdot)\)	16184.cw	34	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)
\(\chi_{16184}(71,\cdot)\)	16184.fk	272	no	\(1\)	\(1\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{101}{272}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{63}{272}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{55}{272}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{91}{272}\right)\)
\(\chi_{16184}(73,\cdot)\)	16184.gb	816	no	\(1\)	\(1\)	\(e\left(\frac{631}{816}\right)\)	\(e\left(\frac{611}{816}\right)\)	\(e\left(\frac{223}{408}\right)\)	\(e\left(\frac{505}{816}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{133}{408}\right)\)	\(e\left(\frac{497}{816}\right)\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{87}{272}\right)\)
\(\chi_{16184}(75,\cdot)\)	16184.dn	48	no	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{16184}(79,\cdot)\)	16184.fy	816	no	\(1\)	\(1\)	\(e\left(\frac{365}{816}\right)\)	\(e\left(\frac{217}{816}\right)\)	\(e\left(\frac{365}{408}\right)\)	\(e\left(\frac{779}{816}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{311}{408}\right)\)	\(e\left(\frac{67}{816}\right)\)	\(e\left(\frac{217}{408}\right)\)	\(e\left(\frac{93}{272}\right)\)

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L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.